MathDB

x_1x_2x_3...x_n <= x_1^2 /2+ x_2^4 / 4 + x_3^8 /8 + ...+1/2^n

Source: Polish MO Recond Round 1980 p2

September 9, 2024

algebrainequalities

Problem Statement

Prove that for any real numbers

x_1, x_2, x_3, \ldots, x_n

the inequality is true

x_1x_2x_3\ldots x_n \leq \frac{x_1^2}{2} + \frac{x_2^4}{4} + \frac{x_3^8}{8} + \ldots + \frac{x_n^{2^ n}}{2^n} + \frac{1}{2^n}